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Let’s check out your problem:
Rewrite the expression in the form
y
n
y^{n}
y
n
.
\newline
Write the exponent as an integer,
fraction
, or an exact decimal (not a mixed number).
\newline
y
7
3
y
1
3
4
=
□
\sqrt[4]{y^{\frac{7}{3}} y^{\frac{1}{3}}}=\square
4
y
3
7
y
3
1
=
□
View step-by-step help
Home
Math Problems
Algebra 1
Powers with decimal and fractional bases
Full solution
Q.
Rewrite the expression in the form
y
n
y^{n}
y
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
y
7
3
y
1
3
4
=
□
\sqrt[4]{y^{\frac{7}{3}} y^{\frac{1}{3}}}=\square
4
y
3
7
y
3
1
=
□
Combine exponents of
y
y
y
:
Combine the exponents of
y
y
y
by adding them, since they are being multiplied and have the same base.
y
(
7
3
)
×
y
(
1
3
)
=
y
(
7
3
+
1
3
)
y^{(\frac{7}{3})} \times y^{(\frac{1}{3})} = y^{(\frac{7}{3} + \frac{1}{3})}
y
(
3
7
)
×
y
(
3
1
)
=
y
(
3
7
+
3
1
)
Add exponents:
Add the exponents
(
7
3
)
(\frac{7}{3})
(
3
7
)
and
(
1
3
)
(\frac{1}{3})
(
3
1
)
.
\newline
(
7
3
)
+
(
1
3
)
=
(
7
+
1
3
)
=
8
3
(\frac{7}{3}) + (\frac{1}{3}) = (\frac{7+1}{3}) = \frac{8}{3}
(
3
7
)
+
(
3
1
)
=
(
3
7
+
1
)
=
3
8
Raise to fourth root:
Now we have
y
8
3
y^{\frac{8}{3}}
y
3
8
under the fourth root, which means we need to raise
y
8
3
y^{\frac{8}{3}}
y
3
8
to the power of
1
4
\frac{1}{4}
4
1
.
y
8
3
4
=
(
y
8
3
)
1
4
\sqrt[4]{y^{\frac{8}{3}}} = \left(y^{\frac{8}{3}}\right)^{\frac{1}{4}}
4
y
3
8
=
(
y
3
8
)
4
1
Apply power rule:
Apply the power rule for exponents
(
a
m
)
n
=
a
m
∗
n
(a^{m})^{n} = a^{m*n}
(
a
m
)
n
=
a
m
∗
n
.
(
y
8
3
)
1
4
=
y
(
8
3
)
∗
(
1
4
)
(y^{\frac{8}{3}})^{\frac{1}{4}} = y^{(\frac{8}{3})*(\frac{1}{4})}
(
y
3
8
)
4
1
=
y
(
3
8
)
∗
(
4
1
)
Multiply exponents:
Multiply the exponents
(
8
3
)
(\frac{8}{3})
(
3
8
)
and
(
1
4
)
(\frac{1}{4})
(
4
1
)
.
8
3
\frac{8}{3}
3
8
∗
\ast
∗
1
4
\frac{1}{4}
4
1
=
8
12
\frac{8}{12}
12
8
=
2
3
\frac{2}{3}
3
2
Write final expression:
Write the final simplified expression.
y
2
3
y^{\frac{2}{3}}
y
3
2
More problems from Powers with decimal and fractional bases
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Evaluate.
\newline
2
2
=
2^2 =
2
2
=
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\newline
(
1
4
)
4
(\frac{1}{4})^4
(
4
1
)
4
= _____
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9
−
61
9^{-61}
9
−
61
?
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Question
Simplify.
\newline
Express your answer using positive exponents.
\newline
r
5
⋅
r
8
r^5 \cdot r^8
r
5
⋅
r
8
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Question
Simplify. Express your answer using a single exponent.
\newline
(
h
2
)
6
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(
h
2
)
6
\newline
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Question
Simplify. Express your answer using positive exponents.
\newline
(
9
p
5
)
(
5
p
8
)
(9p^5)(5p^8)
(
9
p
5
)
(
5
p
8
)
\newline
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Question
Simplify. Express your answer using positive exponents.
\newline
(
2
v
3
)
(
4
v
)
(
5
v
)
(2v^3)(4v)(5v)
(
2
v
3
)
(
4
v
)
(
5
v
)
\newline
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Posted 1 year ago
Question
Simplify. Express your answer using a single exponent.
\newline
(
5
z
8
)
2
(5z^8)^2
(
5
z
8
)
2
\newline
_____________
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Posted 9 months ago
Question
Simplify. Express your answer using positive exponents.
\newline
r
9
⋅
r
8
⋅
r
-
5
r^9 \cdot r^8 \cdot r^{\text{-}5}
r
9
⋅
r
8
⋅
r
-
5
\newline
______
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Posted 9 months ago
Question
Which expression is equivalent to
6
×
6
8
6 \times 6^8
6
×
6
8
?
\newline
Choices:
\newline
1
6
9
\frac{1}{6^9}
6
9
1
\newline
6
8
6^8
6
8
\newline
1
6
8
\frac{1}{6^8}
6
8
1
\newline
6
9
6^9
6
9
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